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Numerov-type methods with minimal phase-lag for the numerical integration of the one-dimensional Schrödinger equation

Methoden vom Numerovschen Typ mit minimaler Phasenverschiebung für die numerische Integration der eindimensionalen Schrödinger-Gleichung

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Abstract

Three Numerov-type methods with phase-lag of order eight and ten are developed for the numerical integration of the one-dimensional Schrödinger equation. One has a large interval of periodicity and the other two areP-stable. Extensive numerical testing on the resonance problem indicates that these new methods are generally more accurate than other previously developed finite difference methods for this problem.

Zusammenfassung

Es werden Methoden vom Numerovschen Typ mit Phasenverschiebung achter und zehnter Ordnung für die numerische Integration der eindimensionalen Schrödinger-Gleichung entwickelt. Eine davon hat ein großes Periodizitätsintervall, die anderen zwei sindP-stabil. Ausgedehnte numerische Tests am Resonanzproblem zeigen, daß diese neuen Methoden für dieses Problem genauer sind als frühere Methoden.

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Authors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Zografou Campus, 157 73, Zografou Athens, Greece

    T. E. Simos & A. D. Raptis

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  1. T. E. Simos
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  2. A. D. Raptis
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Simos, T.E., Raptis, A.D. Numerov-type methods with minimal phase-lag for the numerical integration of the one-dimensional Schrödinger equation. Computing 45, 175–181 (1990). https://doi.org/10.1007/BF02247883

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